On the integral cohomology of BSpin(n)
This paper proves that all torsion in \(H^*(BSpin(n); {\mathbb{Z}})\) has order 2. The analogous results for BO(n) and BSO(n) are due to Borel and Hirzebruch. The proof in this case is similar to the previous cases, by computing the homology of \(H^*(BSpin(n); {\mathbb{Z}}/2)\) with respect to \(Sq^ 1\). The crucial point needed is Quillen's calculation of the mod 2 cohomology.
scientific article; zbMATH DE number 4000988